<i>H</i> _∞ Bipartite Synchronization Composite Antidisturbance Control of Hidden Markov Jump Reaction–Diffusion Neural Networks

This article investigates the problem of composite $H_{\infty }$ control for cooperation-competition networks with hidden Markov jump parameters reaction-diffusions dynamics. Considering the difficulty of directly obtaining the mode information of systems, a continuous-time hidden Markov jump model is employed to represent the joint jump process. Specifically, the hidden process stands for the dynamics of real systems, which cannot be precisely known but can be observed through a detector. Due to the existence of multiple disturbances, the performance of the aforementioned systems can be deteriorated. To reduce the influence of these disturbances, a composite disturbance observer-based controller is constructed, which combines a disturbance observer with a feedback control mechanism. This design significantly improves the robustness and antidisturbance capability of systems. Then, sufficient criteria are derived to guarantee that the bipartite synchronization error system (BSES) is stochastically stable and meets a desired performance index. Finally, the effectiveness of the proposed control method is verified through the performance analysis.